Electrons are normally imagined as particles travelling through a wire. But under the right conditions they can behave collectively like a liquid — complete with microscopic whirlpools. ETH Zurich researchers have now directly observed these electron vortices in graphene at room temperature.

Turn on an electrical device and electrons begin to move.

In an ordinary conductor, such as a copper wire, those electrons repeatedly collide with impurities and imperfections in the material. Some of their energy is converted into heat.

But electrons do not always behave this way.

In the remarkable material known as graphene, electrons can interact so strongly with one another that their collective movement begins to resemble the flow of a liquid.

And liquids can form vortices.

Researchers at ETH Zurich have now succeeded in making these tiny electron whirlpools directly visible. Even more remarkably, they observed them at room temperature.

When electrons behave like water

Graphene consists of a single layer of carbon atoms arranged in a honeycomb-shaped lattice.

Because it is only one atom thick and has unusual electronic properties, graphene has become one of the most intensively studied materials in modern physics.

In a conventional metal, electrons frequently collide with defects in the crystal lattice.

In high-quality graphene, these collisions can become relatively rare. Interactions between the electrons themselves then become much more important.

Under those conditions, electrons can collectively display what physicists call hydrodynamic behaviour.

Instead of thinking only about separate particles moving independently, scientists can describe the electrons almost as though they were a viscous fluid.

Looking for a whirlpool

If electrons really behave like a liquid, theory predicts that they should sometimes form vortices.

The ETH researchers, working in the group of Professor Christian Degen, designed a graphene device specifically to test that prediction.

The conducting graphene strip was only about one micrometre wide.

Along it, the scientists created small circular chambers with diameters ranging from 1.2 to 3 micrometres.

Calculations predicted something very specific: vortices should appear in the smaller chambers but disappear in the larger ones.

That gave the researchers an experimental test.

The problem was seeing something so extraordinarily small.

A quantum sensor inside a diamond

Electrons moving through graphene produce tiny magnetic fields.

To measure those fields, the researchers used a remarkably sensitive quantum sensor.

At the tip of a tiny diamond needle they placed what physicists call a nitrogen-vacancy centre, or NV centre.

This is an atomic-scale defect in the diamond’s crystal structure.

Its quantum state responds to magnetic fields. By manipulating and reading that state using lasers and microwave pulses, researchers can use the defect as an extremely sensitive magnetic-field detector.

The diamond sensor was positioned only about 70 nanometres above the graphene.

That allowed the team to map electrical currents with a spatial resolution of less than 100 nanometres.

Suddenly, the invisible flow of electrons could be reconstructed.

The current flowed backwards

The decisive evidence appeared inside the small circular chambers.

During ordinary electrical transport, the flow inside the chamber should generally follow the direction of the current in the main graphene channel.

But inside the smaller chambers, the researchers measured something very different.

The current reversed direction.

That reversal is the characteristic signature of a vortex.

The electrons were circulating around the chamber like water rotating inside a tiny whirlpool.

And just as predicted, when the chambers became larger, the vortices disappeared.

And it worked at room temperature

Quantum and unusual electronic phenomena often require extremely low temperatures.

Researchers cool materials to temperatures close to absolute zero in order to suppress thermal disturbances that would otherwise obscure delicate effects.

That was not necessary here.

Thanks to the exceptional sensitivity and spatial resolution of their magnetic sensor, the ETH researchers could observe the electron vortices at room temperature.

This makes the result particularly interesting.

The experiment demonstrates that hydrodynamic electron behaviour is not necessarily restricted to exotic cryogenic laboratory conditions.

Whirlpools made from missing electrons

The researchers went one step further.

Electrical conduction in graphene can be dominated either by electrons or by what physicists call holes — effectively missing electrons that behave as positive charge carriers.

By applying an electrical voltage to the graphene, the team could switch between these regimes.

They detected vortices both when transport was dominated by electrons and when it was dominated by holes.

However, near the charge-neutrality point, where small concentrations of electrons and holes coexist, the vortices disappeared.

That observation provides additional information about how hydrodynamic electron flow develops.

A new way of seeing electricity

The research is currently fundamental physics rather than the basis of a new commercial device.

Former ETH doctoral researcher Marius Palm emphasised that many questions remain unanswered, including how collisions between electrons and the boundaries of graphene affect these flow patterns.

But the measurement technique itself opens new possibilities.

The same nanoscale quantum sensor could be used to investigate other unusual forms of electronic transport occurring over distances ranging from tens of nanometres to a few micrometres.

Electricity is stranger than it looks

At human scale, electrical current appears simple.

Connect a wire to a battery and charge flows through it.

At microscopic scale, the picture becomes far richer.

Particles collide.

Quantum effects become important.

And under the right circumstances, billions of electrons stop behaving like an ordinary collection of individual charge carriers and begin moving collectively.

They flow.

They circulate.

They create vortices.

A phenomenon familiar from rivers, oceans and atmospheric storms can therefore emerge in a sheet of carbon only one atom thick.

For the first time, scientists have directly seen those microscopic electrical whirlpools at room temperature.

Source: Based on “Electron vortices in graphene detected,” published by ETH Zurich on 13 May 2024. The underlying research by Marius L. Palm, Chaoxin Ding, William Huxter, Takashi Taniguchi, Kenji Watanabe and Christian L. Degen, “Observation of current whirlpools in graphene at room temperature,” was published in Science, volume 384, pages 465–469.